Problem: Calculate the product below and give your answer in scientific notation. $ {\left(4.3\times 10^{2} \right) \times \left(4.0\times 10^{-3} \right) =\ ?} $
Solution: Start by collecting the significands and exponents. $ ({4.3} \times {10^{2}}) \times ({4.0} \times {10^{-3}}) = ({4.3} \times {4.0}) \times ({10^{2}} \times {10^{-3}}) $ Then multiply each term separately. When multiplying exponents with the same base, add the powers together. $= {17.2} \times {10^{2 \,+\, -3}}$ $= {17.2} \times {10^{-1}}$ To write the answer correctly in scientific notation, the first number needs to be between $1$ and $10$. In this case, we need to move the decimal one position to the left without changing the value of our answer. We can use the fact that ${17.2}$ is the same as ${1.72 \times 10}$ or ${1.72 \times 10^{1}}$. $ = {1.72 \times 10^{1}} \times {10^{-1}} $ $ = 1.72 \times 10^{{1} + {-1}} $ $= 1.72\times 10^{0}$